I think Akira was the first, or nearly so. Unless you want to count videos of "Superbook" when I was a kid (Christian proselytization videos created by Pat Robertson - see wikipedia). I don't.

I didn't like Akira much. There were some other anime I enjoyed quite a bit more that showed at my university, and which I would skip class to watch, but I don't remember any of those (there's one I'd _love_ to get my hands on, but can't find anywhere - involving mechs (what else?), and some prince who pretended to be a completely retarded imbecile, so as to escape destruction by the wicked council or something, who ruled in his stead. He had some super mecha that was hidden underground, and there was some woman with colored hair. I remember her waking up somewhere at the end of the movie, and some children commenting on her hair... I'd love to find this, if somehow these scattered and strange references trigger someone's memory...)

But the first anime I remember watching that really triggered my obsession with them, would have to be Ghost in the Shell. Viewing Princess Mononoke years later certainly didn't hurt either.

Incidentally, I'm one of those weirdos that eventually got into anime through my love of the Japanese language, and not the other way around.

I watched my first anime when I was five. It was either Cardcaptor Sakura or Dragon Ball Z. I really don't remember but I do remember CCS was my fave and DBZ was my brother's. Yeah, those two were popular those days. I'll never get too old for Magical Girls Anime, I swear.

A young girl, with jaded eyes
Stands, and sings a painful tune
For the world to hear and wonder about
Yet no one knows that it is her
That young girl with those eyes
Those terrible, beautiful eyes

My first anime was Eureka Seven. Its still my favorite, and I'm rewatching it for like the bajillionth time lol.

My second, but I haven't finished it, is an old show called Urusei Yatsura.

My third was Birdy the Mighty. Its kind of funny how I came across it because I started learning Japanese, and got some Japanese music to help with that, and found this anime by its 2nd intro song (kiseki by Nirgilis, same guys who did Eureka Seven's 4th OP).

I would have been somewhere about 6-8 years old. We got 3 channels on our antenna in my little town, and if we got up at 6 a.m. Sunday, we could watch cartoons. Black and white cartoon Hercules, Rocket Robin Hood, but my favourite, and my very first anime (though I didn't know it was even called that) was Astro Boy. I loved it then and I really love it now that I own all the DVDs with the subtitles. It's so much better in Japanese...
Yes, very much nostalgic.